The linear regression lines on the natural logarithm plots
of both the compass orientations and the mean side deviations of the Egyptian
pyramids, when plotted against the pyramid numbers, show that they are
mathematically (not physically) related to one another. This
relationship is expressed by the equation

ln (Dev) = -1.27 + 1.17 ln (Or)

where I substituted the numerical values for the intercepts
and slopes.

With explicit statement of all elements the expressions are
as follows:

Note that if B = 1 the expression devolves to Dev = A(Or).
This is extremely interesting for it means that the side deviations are
linearly related to the orientations when B = 1. If B is slightly
different from 1, the relationship over small numbers might appear as linear.

When I first examined the relationship between the two I
did not derive the rigorous mathematical form above. I simply plotted the
numbers from Table II against one another.

Figure Five show this plot with the mean of the absolute
side deviations (folding the negative side of Figure Two over to the positive
side) in parts/10,000 against the mean orientation in minutes of arc west of
north for each structure, This is a linear plot, not a logarithmic plot. (The
plot may appear as linear because B = 1.17.)

This graph shows the strength of correlation for five
structures with measurements all from Petrie. No structure departs more than 5
parts/100,000 on average difference in base length nor more than one minute of
arc in orientation from the calculated regression line. The calculated slope
is 0.49 parts/10,000 per minute of arc. The calculated intercept on the
abscissa is 2.2 minutes. This is the asymptote for Figure 1.

Figure Five raises crucial questions. Its meaning must be
clearly understood.

If the side deviations and the mean orientations are
physically independent of one another the strong linear correlation of Figure
Five must be due to conscious human control.

When I first plotted the points, without benefit of the
derivation, I was surprised at the strength of the correlation. The
correlation certainly could not be due to accident. Some might feel that the
three Giza structures, as a group, are not distributed sufficiently to
demonstrate correlation. Then there would be only three data points showing
correlation, not five. This view assumes unrelated randomness and normal
distribution in the data. However, the calculated correlation coefficient for
all five data points is 0.997. If we group the three Giza structures together
and take their mean value, the calculated coefficient for their correlation
with the Bent wall and Meydum is 0.998. Even more, the calculated correlation
coefficient for the three Giza structures as a group alone is 0.905.
Regardless of how we group the data a high degree of correlation exists among
them. The mathematical equations above show that the strong correlation is not
accidental.

From the mathematical derivation we can recognize the
degree of intelligence necessary to create the correlation.Some might still argue that the correlation may be due to an
inherent relationship in control that caused the sides length deviations to
become smaller as the compass orientations improved. But as I described
above, there is no organic cause why this should be so. The small relative
size of the deviations compared to the side lengths do not support such claim.
Clearly there is a strong, and clever, intelligence on display.

The strong linear correlation cannot be due to anything but
design intent. A predetermined goal of maintaining construction control within
exact equivalent limits of side deviation and compass orientation was executed
by the builders. The correlation could only be by conscious planning and not
merely to uncontrolled improvements in measurement techniques. How could
the builders of Meydum independently have caused the side lengths to deviate
from the mean length in a manner related to mean orientation that would later
correlate with the Bent enclosure wall, Giza 2 and Giza 1 strictly by
accident?

The calculated regression line is very near an analytic
ideal. The dashed line on the graph shows the relationship of Y = -1 + 1/2 X,
where Y is side deviation in parts per 10,000 and X is minutes of arc. Of
course, there can be no negative intercept for absolute values. I am merely
extrapolating to the ordinate to determine the equation of the line. This
equation requires that the builders calculated deviations in parts/10,000 and
minutes of arc in angle.

The designer could “pull” the Giza values slightly to
reinforce the linear regression of Figure Five, while not upsetting the slopes
of Figures Three and Four.

One can see how the designer must have played with the
numbers, seeking both intercepts on Figures Three and Four, and slopes, to
provide numbers that would give the simple equation on Figure Five, while
still making the numbers based on ? and ? apparent to later investigators.

The proposed theoretical regression line is only 2% from
the line calculated from the measured values; the intercept is in similar
proximity. The difference may be due to our measurement limitations and not
due to the construction limitations of the builders. In other words, the
builders are testing the limits of our modern measurement methods.

If we accept that the pole position has moved 0.2' or 0.3'
since construction of the pyramids 4500 years ago the calculated regression
line falls even closer to this analytic ideal.

The simplicity of -1 for the ordinate and a slope of ˝
certainly are not natural or accidental numbers. But this has dramatic impact
on our understanding of the intelligence and mathematical ability of the
designer. We would not be able to discover this relationship except by
plotting it on a graph. Statistical or other mathematical methods would not
make it obvious to us. Therefore, the designer had to use similar graphical
design methods, (or a more sophisticated mathematical equivalent we have not
yet discovered). In turn, this must mean he sat down with ruler and
pencil and consciously laid out such scheme. My graph is merely a
reflection of something he did nearly five thousand years ago.

But even this graph would not be possible if he did not
fully understand exponential and logarithmic relationships. He had to
know that a value of B near one would provide a regression line that appears
linear. This means that he must have attempted many trial plots, with use of
Pi and e to provide numbers we could easily recognize. He had to have great
finesse in higher mathematical relationships. He truly was a genius.

Highly disturbing is the fact that we have not progressed
in our modern thinking to the point that we can arise above intellectual
attitudes about ancient Egyptian cults, nor have we possessed the equivalent
intellectual finesse to see through his design. How many “experts”
are willing to accept that the pyramids were all tied together in one grand
design, or that such ancient knowledge could have existed.

Once again we can see that Cole's data causes the Giza 1
case to fall considerably off the line and again places doubt on his
measurements. If they are more correct than Petrie's they would refute the
correlation for that data point. (I do not show the data for the Giza 1
sockets, which were merely construction control points.)

As we unfold the mathematical relationships we can more
readily recognize why the placement of Giza 2 before Giza 1 in chronology is
forced upon us, even though it violates the accepted chronological order
obtained from historical and archeological data. However, this would not
refute the correlation point on Figure Five since that point is independent of
chronology.